The generator matrix

 1  0  0  0  1  1  1  X  1
 0  1  0  0 a^2*X+1  X a*X+1  1  a
 0  0  1  0 a^2 a^2*X+1 a^2*X+a a^2*X+1  X
 0  0  0  1  1 a^2 X+a X+a^2 a*X+a

generates a code of length 9 over F4[X]/(X^2) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+336x^18+672x^19+42x^20+576x^21+3024x^22+2016x^23+4884x^24+3456x^25+9072x^26+9312x^27+14436x^28+5184x^29+9072x^30+3360x^31+75x^32+18x^36

The gray image is a linear code over GF(4) with n=36, k=8 and d=18.
This code was found by Heurico 1.16 in 0.907 seconds.